Torsional vibration densitometer

ABSTRACT

A direct measurement of density of a fluid is made by coupling the fluid to a rod under torsional oscillation. The frequency of torsional oscillation is maintained at the resonant frequency by sensing the phase difference between the stress in the rod and the current in a driving coil which produces the force to sustain torsional oscillation in the rod. The stress is measured by strain gauges which provide the electrical signal for phase comparison with the driving coil current. The frequency of the current is controlled by a voltage controlled oscillator whose input is derived from the phase comparison to provide a frequency which is at the resonant frequency of the oscillatory rod as modified by the density of the fluid to which it is coupled. The precise relationship between fluid density and resonant frequency is established by calibration.

States Patent Kuenz ler [451 Sept. 12, 1972 [54] TORSIONAL VIBRATIONDENSITOMETER [72] Inventor: Howard W. Kuenzler, South Acton,

Mass.

[73] Assignee: Massachusetts Institute of Technology, Cambridge, Mass.

[22] Filed: Aug. 15, 1969 [21] Appl. No.2 850,534

[52] US. Cl. ..73/32, 73/30, 73/194 B [51] Int. Cl. ..G01n 9/00 [58]Field of Search ..73/32, 30, 67.1, 71.6, 194

[56] References Cited UNITED STATES PATENTS 2,889,702 6/1959 Brooking..73/32 3,444,723 5/ 1969 Wakefield ..73/32 3,516,283 6/1970 Abbotts..73/32 X FOREIGN PATENTS OR APPLICATIONS 731,374 4/1966 Canada ..73/32VARIABLE FREQ. 05C.

FREQUENCY COUNTER Primary ExaminerRichard C. Queisser AssistantExaminer-C, E. Snee, Ill Attorney-Thomas Cooch and Martin M. Santa [5 7]ABSTRACT A direct measurement of density of a fluid is made by couplingthe fluid to a rod under torsional oscillation. The frequency oftorsional oscillation is maintained at the resonant frequency by sensingthe phase difference between the stress in the rod and the current in adriving coil which produces the force to sustain torsional oscillationin the rod. The stress is measured by strain gauges which provide theelectrical signal for phase comparison with the driving coil current.The frequency of the current is controlled by a voltage controlledoscillator whose input is derived from the phase comparison to provide afrequency which is at the resonant frequency of the oscillatory rod asmodified by the density of the fluid to which it is coupled. The preciserelationship between fluid density and resonant frequency is establishedby calibration.

9 Claims, 10 Drawing Figures PATENTEBSEP 12 I972 SHEEI 1 0F 5 FIG.

INVENTOR:'

HOWARD W.' KUENZLER 7d: ATTORNEY PATENTEDsmzmn 3.690.147

- sum 2 or 5 FIG. 2 (b INVENTOR Z HOWARD W. KUENZLER BY Z1: 7;

ATTORNEY PATENTEDSEP 12 i972 INPUT FROM STRAIN GAGE BRIDGE SHEET 3 OF 542 STRAIN GAGE 1 SQUARING AMPLIFIER AMP.

Al PHASE UP DOWN VOLTAGE B v COMPARATOR lf INTEGRATOR OSCILLATOR f VCONTROL VOLTAGE CURRENT OUTPUT TO SOURCE $I TORSION con. 45 4 FIG. 4

INVENTOR:

HOWARD w. KUENZLER BY l al/ ii ATTORNEY 1 TORSIONAL VIBRATIONDENSITOMETER This invention relates to a fluid density measuringapparatus and in particular to a device whose frequency of resonancevaries with the density of the fluid into which it is immersed. Ameasurement of the frequency provides the measure of density.

This invention was made in the course of work done under a contract NonrI841 (74) from the United States Navy.

Many techniques have been proposed and developed to make measurement offluid density. Some techniques are direct and depend upon weighings ofknown volumes or the displacement caused by a reference volume of knowndensity, and others are indirect and depend upon chemical techniques.Their precision and accuracy vary widely. However, they all suffer fromthe same difficulty of requiring a sample of fluid to be taken ndsubjected to laboratory analysis. It is desirable to have equipment thatis both sensitive to small changes in density and which provides acontinuous indication of density in situ.

Therefore, a primary object of this invention is to provide apparatuscapable of making a direct, precise and continuous in situ measurementof the density of a fluid. Such apparatus possesses strong potential foroceanographic applications as well as for a multitude of industrial andmanufacturing processes where the measure of fluid density provides afeedback signal for control of automated sequences.

The objects, features and advantages of any invention will more readilybe understood and appreciated from the following detailed description ofa preferred embodiment thereof selected for purposes of illustration andshown in the accompanying drawing, in which:

FIG. 1 is a pictorial view of the preferred embodiment of the invention.

FIG. 2(a) shows the physical arrangement of the strain gage bridge andFIG. 2(b) shows the circuit connection of the strain gages.

FIG. 3 is a block diagram of the variable frequency oscillator.

FIG. 4 is a schematic of the voltage controlled oscillator.

FIG. 5 is a schematic of the phase comparator.

FIGS. 6, 7, 8, and 9 are circuit diagrams of the strain gage amplifier,the squaring amplifier, the up-down integrator and the current source,respectively.

DESCRIPTION OF THE INVENTION The apparatus of the invention is shown inFIG. 1. Coupling to the fluid whose density is to be measured isprovided by the transducer head 1. The transducer head 1 is a four-vanedstainless steel unit having a bisecting web 2 for rigidity. The head 1is attached between the ends of two cylindrical torsion bars 3 whichprovide a torsional restoring force. Immediately above the head a coil 4of fine magnet wire mounted in a longitudinal slot in bar 3 is wound sothat its plane is parallel to the axis of the torsion bars 3. The entirehead assembly is then mounted rigidly at the bar 3 ends to end plates 5and positioned between the shaped pole pieces 6 of a magnet such thatthe plane of the coil 4 lies within and parallel to the magnetic field 7of the magnet in a fashion similar to a galvanometer movement. A smallcurrent passed through the coil 4 at the torsional resonant frequency byvariable frequency oscillator 8 provides the torque necessary to excitea periodic small amplitude angular displacement of the transducerhead 1. The value of the resonant frequency depends in a simple way uponthe stiffness of the torsion bars and the density of the fluid intowhich the head is immersed. A four-arm active strain gage bridge 9mounted on one torsion bar at its base 10 senses the angulardisplacement and provides an electrical signal for feedback tooscillator 8 to sustain the oscillations. An accurate measurement of theoscillator frequency in frequency counter 11 is converted into anaccurate measure of fluid density by calibration.

THE TRANSDUCER ASSEMBLY The four-vaned head I forces into motion a smallvolume of fluid in its immediate vicinity. When in torsional vibration,each vane 12 resembles a dipole acoustic source. Its four vanes actingtogether in close proximity then approximate an octupole radiator ofacoustic energy. The intensity in the radiation field decreasesinversely as the ninth power of the distance from the head 1, makingthis design inefficient as an acoustic source. It is just thischaracteristic, however, that makes the design highly desirable as adensity transducer. It ensures that the volume of fluid influenced bytransducer motions is of the order of the dimensions of the head 1, andtherefore ensures that the transducer responds only to changes in thelocal fluid density. Because the decay of field intensity with distanceis caused by phase interference rather than by spherical spreading orabsorption phenomena, the effects of small changes in acousticparameters on the size of the virtual mass can be safely ignored.Comparisons of the resonant frequency in water with that in air haveshown that the effective diameter of the virtual mass of fluid entrainedis only percent of the diameter'of the transducer head itself.

Because the acceleration of every portion of the transducer head issufficiently low, there is no danger of cavitation within the fluid.

The transducer head 1 comprising the axial vanes 12 and the transversestiffening web 2 is machined from a solid block of No. 304 stainlesssteel for dimensional stability and for resistance to attack by seawater. The surface may be passivated to eliminate frequency drift iflong exposure to corrosive environments is expected. Although stainlesssteel has a moderate thermal expansion coefiicient, its effect onfrequency is eliminated by properly choosing the thermoelasticcoeflicient for the torsion bars. The thickness of the vanes and web aredesigned so that flexure of the head itself at any point contributesless than 1 percent to the total displacement due to twisting of thetorsion bars. Greater flexure would be permissible but would reduce thecoupling to the fluid.

The torsion bars 3 are rigidly attached at their ends to the two endplates 5, and the torsion coil 4 is positioned between the shaped polepieces 6 in the magnetic field 7 near the head 1 which connects bars 3.The framework supporting the end plates 5 is rigid so that there isnegligible twisting in it when torque is applied to the bars 3 at thetransducer head by coil 4. The head 1 is open to allow fluid to flushfreely through the transducer head. This feature insures a rapidresponse to density changes in the surrounding fluid.

Although the preferred embodiment of the invention has employed atorsionally resonant transducer comprising a rod to which vanes areattached to provide a transducer of sufficiently high Q and sufficientlylow inertia for desirable operation, it is apparent that othermechanically resonant transducer assemblies could be fabricated by thoseskilled in the art to provide the function of transducer of thepreferred embodiment with the desired properties. As an example, amagnetostrictive or piezoelectric rod, of configuration such as that ofthe preferred embodiment, in longitudinal vibration instead of torsionaland with a vane in a plane transverse to the axis of the rod wouldfunction adequately. A plurality of vanes spaced along the axis of therod would appear to provide a localized field of influence as in themulti-vaned transducer of the preferred embodiment.

Another example of a suitable transducer would be one in which the rodis eliminated as the element providing the spring constant of themechanically resonant system. Instead, a vane which provides the dualfunction of the spring constant together with coupling to the fluidmight be used. The vane may be magnetos trictive or it may bemechanically secured to an electrical coil which when energized in thepresence of a magnetic field as in the preferred embodiment causes thevane to vibrate at the frequency of energization.

It is apparent from the above two examples that alternative embodimentsof the mechanical transducer are available to those skilled in the artwithout departing from the scope of the invention. What is desired is amechanically resonant device capable of being coupled to a fluid,capable of being electrically driven at the resonant frequency andcapable of having its strain provide an electrical signal.

STRAIN GAGE BRIDGE Angular displacement of the transducer head is sensedby a four-arm active semiconductor strain gage bridge 9 shown in FIG. 2.The gages A, B, C, and D are mounted on opposite faces of two flats atthe base 10 of one of the torsion bars 3. Their orientation at 45 withrespect to the torsion bar axis is shown on FIG. 2(a) and theirelectrical connection as in FIG. 2(b) give maximum sensitivity totorsional stresses and greatly attenate signals due to flexure of thebar. This bridge arrangement greatly reduces the possibility thatflexural modes of oscillation will be excited. The wires 21, 22connected to the bridge are conveniently brought out through radialholes (not shown) to the center of bar 3 and thence out through an axialhole 23. The wires 33 to coil 4 are also brought out through hole 23 sothat they have negligible effect on the amount of inertia of thetransducer assembly. Wires 21 are connected to a source of d.c.electrical energy E for the bridge, and wires 22 provide an outputcontrol signal from the bridge 9 to variable frequency oscillator 8.

Variable Frequency Oscillator Resonance is sustained by feedback frombridge 9 to torsion coil 4 through variable frequency oscillator 8 asshown in the block diagram in FIG. 3. The sequence of events by whichthe resonant frequency is achieved occurs as follows. Thevoltage-controlled oscillator 31 begins at a frequency that is near tobut not exactly at the resonant frequency. It provides a sawtooth signalon line 45 to the current source 32 which in turn provides a sawtoothcurrent through lines 33 to the torsion coil 4. The torque produced bythis current forces angular displacements of the transducer head 1. Thestrain gage bridge 9 provides a signal proportional to and in phase withthe displacements.

After the bridge signal is amplified by the strain gage amplifier 34, itis converted to a square wave in circuit 35 and applied as one input 39of the phase comparator 36. A square wave from the voltage controlledoscillator 31 shifted in phase with respect to the sawtooth, is appliedas the other input 37 of the phase comparator. Once each cycle of thesquare wave the phase comparator 36 generates a pulse 38 of constantamplitude whose width is proportional to the difference in phase betweenthe two inputs 37, 39. If the phase is leading, the pulse 38 appears onthe one line, and vice versa. The up-down integrator 40 is a standarddifference integrator which accepts these pulses and adjusts its outputlevel 41 accordingly so as to bring the voltage-controlled oscillator 31to the exact resonant frequency.

This type of proportional control in the feedback loop produces a verytightly locked resonant system. Because a correction is applied onceeach cycle, any instantaneous error is reduced by averaging over anumber of cycles. Having a local oscillator whose frequency need beadjusted only slightly has the added benefit of allowing the system toadjust rapidly to sudden changes in fluid density.

VOLTAGE CONTROLLED OSCILLATOR The voltage controlled oscillator 31 ofFIG. 4 consists primarily of two operational amplifiers A,, A twoidentical switching transistors T,, T and two identical directing diodesD,, D,,. Amplifier A, is connected as an integrator with feedbackcapacitor C, and input resistors R Amplifier A is connected as a voltagecomparator with hysteresis. Diodes D, and D protect A from excessiveinput potential. Resistors R and R serve to balance the resistance ateach input and to prevent common mode latch-up of the amplifier.Switching transistor T, allows the input current to A, to beperiodically reversed. T which is held in saturation by a constantpotential V serves to compensate for the effect of collector-to-emittersaturation voltage of transistor T,.

The voltage E, at the output 45 of A, is a triangular waveform. itsamplitude depends upon the output saturation voltage iV, of amplifier Aand upon the voltage divider ratio of resistors R and R.,. The frequencyis governed by the magnitude of the input voltage V,, by the voltagedivider ratio of R and R and by the R C, product associated withamplifier A,.

The two resistors labelled R, act as a voltage divider for the inputvoltage V, in series with the collector-toemitter saturation voltage 6of transistor T Therefore, the voltage across C is The two diodes D, andD direct the current flow into and out of amplifier A,. Because they areidentical units, they exhibit identical forward voltage drops 6 underidentical conditions.

The following events occur during one cycle of the voltage controlledoscillation. Suppose the output of The inflow of current I through R,and D causes a negative-going ramp E, to appear at the output of A,.When this ramp reaches the potential V, R.,/(R +R the output of A goesinstantaneously to +V,, causing T to saturate. 1 goes to zero and Ibegins to flow through R D and T,. Its magnitude is This current causesa positive-going ramp to appear at the output of A Because I 1 dE /dtfor the negative-going ramp equals dE /dt for the positive-going ramp.Therefore, E is a triangular waveform. When E reaches the potential +VR,/(R +R.,) the output of A goes instantaneously to -V,. This turns offtransistor T,, and the cycle begins again.

With I =1 E l, the period T of oscillation can be written as The squarewave output 53 of amplifier A maintains a precise 90 phase lead over thetriangular output 45 of amplifier A regardless of frequency.

Although the voltage-controlled oscillator of the preferred embodimenthas provided a sawtooth waveform at output 45, a conventional voltagecontrolled oscillator which provides a sine wave output would be aseffective. It is within the capabilities of those skilled in the art toprovide a conventional voltagecontrolled sinusoidal drive currenttogether with the 90 phase shifted square wave output by circuitry otherthan that of the preferred embodiment.

PHASE COMPARATOR The phase comparator of FIG. consists of six twoinputNAND gates ND, six inverting amplifiers I and a two input set-reset flipflop FF. Input square waveforms A and B on lines 37, 39 are timesequences of logical ones and logical zeros having voltage levelsappropriate for the logic gates used. Standard logic symbology is usedin this discussion so that for instance, A means the complement of A andAB means the complement ofA AND B.

The operation of the phase comparator depends upon the fact that thesequence of logical events generated from the two input signals A and'Boccur in one order if the phase of A leads that of B and in a differentorder if the phase of B leads that of A. Thus, when the phase of input Ais leading the phase (3 input B,the sequence of logical events is A-B,A-B, A-B, A-B, A'B, A-B, etc. in continuous repetition. When the input Bleads A, the second and fourth logical events in the above sequence arei n te13hanged so Eat the sequence becomes A-B, A-B, A-B, A-B, A-B, AB,etc. A cycle for the phase comparator begins with the logical event ABand terminates with the logical event A-B.- During that interval of timeonly two other logical events may occur, the event A-B if A leads B orthe event A- B if B leads A. The duration of the events KB or AB is a R1 8 a+ 4 I direct indication of the amount of phase difference betweenthe two input signals. By suitably gating the signals, a logical onevoltage level coincident with the event AB is made to appear at one ofthe output lines when A leads B a nd a similar voltage level coincidentwith the event AB is made to appear at the other output line if B leadsA.

The phase comfirison begins with the generation of the logic signal A-Bby NAND gate ND (Refer to schematic diagram). This signal sets flip-flopFF output to a one" output state which in turn enables one input of NDand ND If signal A leads signal B, then the nei t event after A-B istheevent AB. The logic signal A'B, after being generated in complement formby ND,, is passed through I gated through ND, and presented at theoutput of 1 Its duration is an indication of the amount that signalAleads signal B. Immediately after K8, the signal AB is generated incomplement from by ND This signal resets FF which in turn disables NANDgates ND and ND Once these two gates have been disabled, the next eventAB, which would give an erroneous output, is blocked from reaching I If,however, signal B leads signal A, the event AB occurs after A-B.Flip-flop FF which is set again by the occurence of AB, enables ND andND,,. After being generated in complement form by ND the logic signal ABis passed through 1,, gated through ND and presented at the output of IIts duration is an indication of the amount that signal B leads signalA. Immediately following A-B, the signal AB is generated in complementform by ND, and is used to reset FF. This disables ND, and ND, until thenext occurrence of AB and precludes any erroneous signal at I The outputfrom either 1 or 1 is, therefore, a train of pulses whose width isproportional to the instantaneous phase difference between input signalsA and B. If A leads B, the pulse train appears at I output 51 and if Bleads A, it appears at 1 output 52. The pulse trains are in a formsuitable for application to feedback elements for system control. Thediodes D and D serve only to remove some small residual voltage thatappears at the outputs of I and I Phase error allowed by this type ofphase comparator depends primarily upon small differences in thepropagation delay time of the particular NAND gates used. This error-isminimized, however, by complete component symmetry in the design.

ASSOCIATED CIRCUITRY The circuit diagrams of the strain gage amplifier,squaring amplifier, the up-down integrator and the current source ofFIGS. 6, 7, 8, and 9, respectively have been included for completenessof the circuitry comprising the variable frequency oscillator 8 of thepreferred embodiment. Commercially available operational amplifiers OP.AMP. were used to perform the desired functions. Other circuits toprovide these functions could be provided by those skilled in the art.

TORSIONAL OSCILLATIONS When a mechanical system such as the onedescribed having a transducer'with moment of inertia I and torsion barswith spring constant k is excited by a sinusoidal torque of amplitude fand radian frequency to, its angular displacement 0. is given by thedifferential equation,

d a do J d7 where t is time and p. is the damping coefficient. Thecomplex amplitude 0(a)) is found to be,

If the frequency is adjusted so that the angular response lags theapplied torque by 90, then the real part of (2) must be zero, so that,

a.\=(K/I) 01,. (3) Equation (3) defines the resonant frequency. Itshould be noted that when torhional oscillations are sustained such that0 lags r by 90, the resonant frequency is not dependent upon ;1.. Thisensures that to, will not be a function of dissipation in the system. Interms of its electrical analog, 0:, is called the unity power factorfrequency because at this frequency current and applied voltage are inphase.

When the transducer is placed into a fluid, its effective moment ofinertia is increased because of the virtual mass of entrained fluid. Themoment of inertia of the virtual mass is directly proportional to itsdensity p. The system is sustained in resonance by automaticallyadjusting the driving frequency so as to maintain the 90 phase anglebetween torque and angular response. Sensing of an off-resonance errordepends upon the fact that the phase angle between 1- and 0(a)) changesrapidly near (o The rate of change of the phase angle with frequency isdirectly proportional to the mechanical Q and inversely proportional tothe resonant frequency. The mechanical Q of the system should be as highas possible for best results. The mechanical Q is directly proportionalto the spring constant k of the torsion bars and inversely proportionalto the products of the resonant frequency and the damping coefficient p.of the fluid.

When the system operates precisely at 0),, there is no change in theresonant frequency if p. changes. However, if the phase differencebetween torque and response is not quite 90, there will be some error.The percent change in frequency compared to the percent change in p.decreases with increasing system Q. This is one advantage of making Q aslarge as possible.

Another advantage of a high Q system is that the amount of torquerequired to sustain an angular displacement 0 at resonance is decreasedin proportion to Q.

As an example of a Q value which is attainable, the preferred embodimenthad a Q of 239 when the vanes were immersed in water at a resonantfrequency of 477 Hz. The moment of inertia of the transducer assemblywas approximately three fourths of the inertia when immersed in water.Consistent with the desire to have vanes with mechanical stiffness, toprovide good coupling to the fluid the inertia of the transducerassembly should be as small as possible with respect to the inertia ofthe fluid entrained by the transducer head since sensitivity to changesin fluid density is thereby increased.

The torque is produced by the simple technique of current interactionwith a magnetic field as is done in galvanometer movements. As shown inFIG. 1, a coil 4 is placed with its plane parallel to the magneticfield. When the mechanical system has a large Q, sufficient torque isprovided by this technique to drive the system.

TEMPERATURE COMPENSATION The thermoelastic coefficient as used here isdefined as the change in elastic modulus without correction for theeffects of thermal expansion. The moment of inertia I of the transducerhead is proportional to its height h and the fourth power of its radiusR. The expression for angular resonant frequency a, is proportional tothe square root of the elastic modulus k divided by the moment ofinertia I. When in, is differentiated with respect to temperature T, theresulting expression shows that the thermoelastic coefficient of thematerial for the torsion bar can be chosen such that it cancels thethermal expansion coefficient of the entire transducer assembly thusgiving a near-zero overall sensitivity to temperature changes. Such amaterial is Ni-Span-C Alloy 902, a product of the International NickelCompany. With cold work and heat treatment, this alloy can be given awide range of coefiicients as shown in Technical Bulletin T-3 lInternational Nickel Co., Inc., 1963.

OTHER FORMS OF RESONANCE Although the preferred embodiment of theinvention has used a resonance defined as that frequency at which thephase angle between the applied torque and the resulting angulardisplacement is there are other resonances which could also be utilized.The resonance defined by the 90 phase relationship referred to above hasthe advantage over the two resonances to be now discussed in that thefrequency of resonance is independent of linear damping effects of thefluid.

Another form of resonance which could be used in this invention is onewhere the frequency is adjusted to produce the maximum displacement ofthe mechanically resonant fluid coupled system. This form of resonanceis sensitive to changes in the fluid viscosity so that apparatus wouldhave to be calibrated for the viscosity of the fluid whose density isbeing determined. The strain gage output of the device described in thepreferred embodiment would produce a signal to a voltage controlledoscillator in a feedback loop such that the frequency of oscillationwould maximize the strain gage output signal. Although there may beapplications where this type of resonance would be applicable, it isbelieved that apparatus incorporating amplitude resonance would not beas sensitive to density changes as that of the preferred embodiment.

An alternative form of resonance also responsive to fluid viscosity aswell as density is that of the natural vibration frequency. The torsionbar of the preferred embodiment is caused to undergo an initial physicaldisplacement from its quiescent position. The initial displacement ofthe bar may be produced by applying a current to coil 4. Upon itsrelease from its displaced position, the bar and its attached vanes willexperience a damped oscillation whose frequency may be determined. Theoutput of the strain gage could be used to provide the dampedoscillation frequency. Frequency locking techniques, well known to thoseskilled in the art, may be employed to extend the effective timeduration of the frequency of the decaying oscillation for convenience ofmeasurement. This type of resonance also produces a frequency which issensitive to both density and viscosity of the fluid being measured andthus the viscosity of the fluid is required for accurate densitymeasurements.

It will thus be seen that the objects set forth above, among thoseapparent from the preceding description, are efficiently attained and,since certain changes may be made in the above constructions withoutdeparting from the scope of the invention, it is intended that allmatter contained in the above description or shown in the accompanyingdrawings shall be interpreted as illustrative and not in a limitingsense.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed, and all statements of the scope of the invention which, as amatter of language, might be said to fall therebetween.

Having described my invention, what I claim as new and desire to secureby Letters Patent is:

1. Apparatus for determining the density of a fluid comprising:

a mechanically oscillatory member,

means for coupling said fluid to said member,

means for causing said member to oscillate at its resonant frequencycomprising,

a voltage controllable electrical oscillator,

means for applying a sinusoidal torque to said mechanical member, meansfor providing a first alternating electrical signal which is in phasewith the applied torque, means for sensing a second alternatingelectrical signal which is in phase with the strain of the mechanicalmember, means for comparing the phase of said first and secondelectrical signals to provide a control electrical signal responsive tothe phase difference,

and means for providing said control signal to said electricaloscillator to control its frequency to maintain the compared phasedifference at 90,

means for measuring the frequency of said electrical oscillator wherebythe density of the fluid is determined.

2. The apparatus of claim 1 wherein said mechanically oscillatory membercomprises a rod rigidly attached to a frame at least at one end, saidrod being free to undergo torsional oscillation,

and said fluid coupling means comprises at least one radially projectingvane attached to said rod other than at said frame.

3. The apparatus of claim 2 wherein there are a plurality of said vanesattached to said rod at the same longitudinal position and spacedequally in angle around the circumference of said rod.

4. The apparatus of claim 3 wherein the plane of said vanes is axiallyand radially oriented with respect to the axis of said rod.

5. The apparatus of claim 4 comprising in addition said rod beingrigidly attached at both ends to said frame,

and said vanes are attached centrally along the le th f said rod. Tii apparatuS of claim 3 wherein said plurality of vanes are of openconfiguration to allow free flow of fluid to said vanes.

7. The apparatus of claim 5 wherein said plurality of vanes numbersfour.

8. The apparatus of claim 2 wherein said means for causing said rod totorsionally oscillate at the resonant frequency comprises a coilattached to said rod,

a magnet providing a magnetic field for said coil,

the plane of said coil being in the direction of said magnetic field andalong the axis of said rod,

means for providing an alternating current to said coil at the frequencyof resonance.

9. The apparatus of claim 8 wherein said means for providing analternating current in said coil at the frequency of resonance comprisesa voltage-controlled oscillation means connected to said coil to providesaid alternating current,

a strain sensing means attached to said rod to provide an alternatingcurrent signal responsive to the strain of said rod,

a phase comparison means connected to said coil and said sensing meansfor determining the phase difference between the alternating current ofsaid coil and the voltage of said strain sensing means and for providingan electrical output to said voltage controlled oscillator to controlits frequency to cause said measured phase difference to be

1. Apparatus for determining the density of a fluid comprising: amechanically oscillatory member, means for coupling said fluid to saidmember, means for causing said member to oscillate at its resonantfrequency comprising, a voltage controllable electrical oscillator,means for applying a sinusoidal torque to said mechanical member, meansfor providing a first alternating electrical signal which is in phasewith the applied torque, means for sensing a second alternatingelectrical signal which is in phase with the strain of the mechanicalmember, means for comparing the phase of said first and secondelectrical signals to provide a control electrical signal responsive tothe phase difference, and means for providing said control signal tosaid electrical oscillator to control its frequency to maintain thecompared phase difference at 90*, means for measuring the frequency ofsaid electrical oscillator whereby the density of the fluid isdetermined.
 2. The apparatus of claim 1 wherein said mechanicallyoscillatory member comprises a rod rigidly attached to a frame at leastat one end, said rod being free to undergo torsional oscillation, andsaid fluid coupling means comprises at least one radially projectingvane attached to said rod other than at said frame.
 3. The apparatus ofclaim 2 wherein there are a plurality of said vanes attached to said rodat the same longitudinal position and spaced equally in angle around thecircumference of said rod.
 4. The apparatus of claim 3 wherein the planeof said vanes is axially and radially oriented with respect to the axisof said rod.
 5. The apparatus of claim 4 comprising in addition said rodbeing rigidly attached at both ends to said frame, and said vanes areattached centrally along the length of said rod.
 6. The apparatus ofclaim 3 wherein said pluraLity of vanes are of open configuration toallow free flow of fluid to said vanes.
 7. The apparatus of claim 5wherein said plurality of vanes numbers four.
 8. The apparatus of claim2 wherein said means for causing said rod to torsionally oscillate atthe resonant frequency comprises a coil attached to said rod, a magnetproviding a magnetic field for said coil, the plane of said coil beingin the direction of said magnetic field and along the axis of said rod,means for providing an alternating current to said coil at the frequencyof resonance.
 9. The apparatus of claim 8 wherein said means forproviding an alternating current in said coil at the frequency ofresonance comprises a voltage-controlled oscillation means connected tosaid coil to provide said alternating current, a strain sensing meansattached to said rod to provide an alternating current signal responsiveto the strain of said rod, a phase comparison means connected to saidcoil and said sensing means for determining the phase difference betweenthe alternating current of said coil and the voltage of said strainsensing means and for providing an electrical output to said voltagecontrolled oscillator to control its frequency to cause said measuredphase difference to be 90*.